
where \(\mathbf {v}_\mathbf {k}^\chi \)  is the band velocity, \(\Omega ^\chi = -\chi \mathbf {k} /2k^3\)  is the Berry curvature, and \(\mathcal {D}^\chi = (1+e\mathbf {B}\cdot \Omega ^\chi /\hbar )^{-1}\) . The self-rotation of Bloch wavepacket also gives rise to an orbital magnetic moment (OMM) [1]} \(\mathbf {m}^\chi _\mathbf {k}\) . In the presence of magnetic field, the OMM shifts the energy dispersion as \(\epsilon ^{\chi }_{\mathbf {k}}\rightarrow \epsilon ^{\chi }_{\mathbf {k}} - \mathbf {m}^\chi _\mathbf {k}\cdot \mathbf {B}\) . Interestingly, the Berry curvature and the orbital magnetic moment turn out to be independent of the tilting of the Weyl cones.
